Smoothed Pseudo Wigner-Ville Distribution Research Articles

The Parameter Estimation of Non-Cooperative Frequency Hopping Signals Based on the Algorithm of RSPWVD

How to get good time-frequency distribution of FH signals is crucial to detect and to trace the FH signals. The theory about the rearrangement of time-frequency distribution is summarized in the paper, then the basic principle of detecting the signals using the algorithm of rearrangement of the smooth pseudo Wigner-Ville distribution (RSPWVD) is analyzed in detail, and the algorithm expression are given at the same time. The analysis results show that the RSPWVD algorithm not only has more ideal anti-jamming effects, but also can enhance the time-frequency aggregation of the signal, so the signal parameters are estimated more accurately. In the end, the computer simulation is shown to test the feasibility and effectiveness of the algorithm.

Automated Fault Classification of Reciprocating Compressors from Vibration Data: A Case Study on Optimization Using Genetic Algorithm

This article deals with automated fault classification of reciprocating compressors from vibration data. The genetic algorithm was applied to automate the process. A total of 15 fault cases based on practical observation of the machine faults was considered. Vibration data for the various fault cases were collected and processed using the time-frequency analysis, namely the short time Fourier transform (STFT), the smoothed pseudo Wigner-Ville distribution (SPWVD), and the reassigned smoothed pseudo Wigner-Ville distribution (RSPWVD), due to the non-stationary vibration characteristics of the system analyzed. The fault features for the formidable amount of time-frequency data were extracted first and fed into an artificial neural network for fault classification. It is demonstrated in this work that it is feasible to apply the genetic algorithm to automate the fault classification process and thereby minimize the requirement for intervention from the human experts.

Blind Separation of Synchronous-networking Frequency Hopping Signals based on Time-frequency Analysis

A novel method on smoothed-pseudo Wigner-Ville Distribution (SPWVD) to extract single-source zone of the synchronous-networking frequency hopping (FH) signals is proposed in this paper. Since the hop rate and hop period of synchronous-networking FH signals are the same, the method is applied combining with these characteristics. Compare with other methods such as independent component analysis (ICA), the algorithm takes the advantage of the sparse distribution of FH signal in frequency. Then the blind separation algorithm of FH signals with time-frequency ration of matrix (TIFROM) based on short time Fourier transform (STFT) is improved. Simulation results show that the proposed algorithm is effective in the separation of synchronous-networking FH signals, even though the interval between FH signals is relatively small.

Automatic classification of sleep stages based on the time-frequency image of EEG signals

In this paper, a new method for automatic sleep stage classification based on time-frequency image (TFI) of electroencephalogram (EEG) signals is proposed. Automatic classification of sleep stages is an important part for diagnosis and treatment of sleep disorders. The smoothed pseudo Wigner–Ville distribution (SPWVD) based time-frequency representation (TFR) of EEG signal has been used to obtain the time-frequency image (TFI). The segmentation of TFI has been performed based on the frequency-bands of the rhythms of EEG signals. The features derived from the histogram of segmented TFI have been used as an input feature set to multiclass least squares support vector machines (MC-LS-SVM) together with the radial basis function (RBF), Mexican hat wavelet, and Morlet wavelet kernel functions for automatic classification of sleep stages from EEG signals. The experimental results are presented to show the effectiveness of the proposed method for classification of sleep stages from EEG signals.

Approach to Extraction of Incipient Fault Features on Unstable Rotating Rolling Bearings Based on Time-Frequency Order Tracking and SPWVD

Frequency-smear phenomenon caused by fierce rotating speed variation made it difficult to extract the fault features of the rolling bearing. An approach based on time-frequency order tracking and SPWVD was proposed in this paper. The influence of speed variation was reduced by resampling the time-domain non-stationary signal at constant angle increments with order tracking analysis. The precision of instantaneous frequency estimation (IFE) in time-frequency order tracking was improved by the use of Smoothed Pseudo Wigner-Ville Distribution (SPWVD). The simulation signal and experiment on test-rig revealed that the proposed method was more effective than the traditional order tracking in clarifying incipient fault.

Influence of Running Stride Frequency in Heart Rate Variability Analysis During Treadmill Exercise Testing

The analysis and interpretation of heart rate variability (HRV) during exercise is challenging not only because of the nonstationary nature of exercise, the time-varying mean heart rate, and the fact that respiratory frequency exceeds 0.4 Hz, but there are also other factors, such as the component centered at the pedaling frequency observed in maximal cycling tests, which may confuse the interpretation of HRV analysis. The objectives of this study are to test the hypothesis that a component centered at the running stride frequency (SF) appears in the HRV of subjects during maximal treadmill exercise testing, and to study its influence in the interpretation of the low-frequency (LF) and high-frequency (HF) components of HRV during exercise. The HRV of 23 subjects during maximal treadmill exercise testing is analyzed. The instantaneous power of different HRV components is computed from the smoothed pseudo-Wigner-Ville distribution of the modulating signal assumed to carry information from the autonomic nervous system, which is estimated based on the time-varying integral pulse frequency modulation model. Besides the LF and HF components, the appearance is revealed of a component centered at the running SF as well as its aliases. The power associated with the SF component and its aliases represents 22±7% (median±median absolute deviation) of the total HRV power in all the subjects. Normalized LF power decreases as the exercise intensity increases, while normalized HF power increases. The power associated with the SF does not change significantly with exercise intensity. Consideration of the running SF component and its aliases is very important in HRV analysis since stride frequency aliases may overlap with LF and HF components.

Time–frequency manifold correlation matching for periodic fault identification in rotating machines

For rotating machines, the localized faults of key components generally represent as periodic transient impulses in vibration signals. The existence of background noise will corrupt transient impulses in practice, and will thus increase the difficulty to identify specific faults. This paper combines the concepts of time–frequency manifold (TFM) and image template matching, and proposes a novel TFM correlation matching method to enhance identification of the periodic faults. This method is to conduct correlation matching of a vibration signal in the time–frequency domain by using the TFM with a short duration as a template. By this method, the time–frequency distribution (TFD) of a vibration signal is firstly achieved by the Smoothed Pseudo-Wigner–Ville distribution (SPWVD) method. Then the TFM template is learned to do correlation matching with the TFD of the analyzed signal. Finally, the ridge is extracted from the correlation matching image and the ridge coefficients are analyzed for periodic fault identification. The proposed method takes advantages of the TFM in noise suppression and template matching in object enhancement, and can enhance the fault impulses of interest in a unified scale. The novel method is verified to be superior to traditional enveloping method with providing smoother and clearer fault impulse component via applications to gearbox fault detection and bearing defect identification.

A novel approach for detection of deception using Smoothed Pseudo Wigner-Ville Distribution (SPWVD)

For many years, the uncertainty of lie-detection systems has been one of the concerns of defense related agencies. Clearly the results of these systems must be generalized by a high value of accuracy to be acceptable by judicial systems. In this paper, a new method based on P300-based component has been proposed for lie-detection. In this regard, the test protocol is designed based on Odd-ball paradigm concealed information recognition. This test was done on 32 people and their brain signals were acquired. After preprocessing, the classic features are extracted from each single trial. After that, time-frequency (TF) transformation is applied on the sweeps and TF features are produced thereupon. Then, the best combinational feature vector is selected in order to improve classifier accuracy. Finally, Guilty and Innocent persons are classified by KNN and MLP. We found that combination of Time-Frequency and Classic features have better ability to achieve higher amount of accuracy. The obtained results show that the proposed method can detect deception by the accuracy of 89.73% which is better than other previously reported methods.

Reservoir information extraction using a fractional fourier transform and a smooth pseudo Wigner-Ville distribution

Currently, it is difficult for people to express signal information simultaneously in the time and frequency domains when analyzing acoustic logging signals using a simple-time or frequency-domain method. It is difficult to use a single type of time-frequency analysis method, which affects the feasibility of acoustic logging signal analysis. In order to solve these problems, in this paper, a fractional Fourier transform and smooth pseudo Wigner-Ville distribution (SPWD) were combined and used to analyze array acoustic logging signals. The time-frequency distribution of signals with the variation of orders of fractional Fourier transform was obtained, and the characteristics of the time-frequency distribution of different reservoirs under different orders were summarized. Because of the rotational characteristics of the fractional Fourier transform, the rotation speed of the cross terms was faster than those of primary waves, shear waves, Stoneley waves, and pseudo Rayleigh waves. By choosing different orders for different reservoirs according to the actual circumstances, the cross terms were separated from the four kinds of waves. In this manner, we could extract reservoir information by studying the characteristics of partial waves. Actual logging data showed that the method outlined in this paper greatly weakened cross-term interference and enhanced the ability to identify partial wave signals.

Time–Frequency Analysis Based Flow Regime Identification Methods for Airlift Reactors

The flow regime transitions in an airlift reactor were investigated based on pressure fluctuation signals. Two time–frequency analysis methods, i.e., Wigner–Ville distribution and wavelet transform, were used to extract flow regime characteristics from pressure signals. The main frequency derived from the smoothed pseudo-Wigner–Ville distribution of the pressure signal was used to quantify flow regime transitions in the reactor. Two flow regime transition points were successfully detected from the evolution of main frequencies of pressure signals. In addition, the local dynamic characteristics of the pressure signal at different frequency bands were analyzed by use of the wavelet transform. A new flow regime identification method based on the wavelet entropy of the pressure signal was proposed. This method was confirmed to be reliable and efficient to detect flow regime transitions in the reactor.

Generation and detection of higher-order mode clusters of guided waves (HOMC-GW) using meander-coil EMATs

This paper reports on a new means of generating higher-order mode clusters of guided waves (HOMC-GW) using a meander-coil (MC) electromagnetic acoustic transducer (EMAT) in plates at frequencies significantly higher than the lower-order plate modes. These wave modes are considerably less dispersive and they occur at much higher frequency-thickness (f x d) products. Our studies cover the f x d range of 13 to 20 MHz·mm. Experimental measurements were carried out on Al plate samples of different thicknesses using three different EMAT coil periods. To understand the generation and propagation characteristics of HOMC-GW with EMATs, several simulations were carried out using 2-D finite element models at different f x d products. These simulations captured all features observed in the experiments. The time-frequency smoothed pseudo Wigner-Ville distribution (SPWVD) was used to analyze the HOMC-GW modes. Defect detection measurements using HOMC-GW generated using EMATs were made on Al plates with machined defects.

Assessment of the dynamic interactions between heart rate and arterial pressure by the cross time–frequency analysis

In this study, a framework for the characterization of the dynamic interactions between RR variability (RRV) and systolic arterial pressure variability (SAPV) is proposed. The methodology accounts for the intrinsic non-stationarity of the cardiovascular system and includes the assessment of both the strength and the prevalent direction of local coupling. The smoothed pseudo-Wigner–Ville distribution (SPWVD) is used to estimate the time–frequency (TF) power, coherence, and phase-difference spectra with fine TF resolution. The interactions between the signals are quantified by time-varying indices, including the local coupling, phase differences, time delay, and baroreflex sensitivity (BRS). Every index is extracted from a specific TF region, localized by combining information from the different spectra. In 14 healthy subjects, a head-up tilt provoked an abrupt decrease in the cardiovascular coupling; a rapid change in the phase difference (from 0.37 ± 0.23 to −0.27 ± 0.22 rad) and time delay (from 0.26 ± 0.14 to −0.16 ± 0.16 s) in the high-frequency band; and a decrease in the BRS (from 23.72 ± 7.66 to 6.92 ± 2.51 ms mmHg−1). In the low-frequency range, during a head-up tilt, restoration of the baseline level of cardiovascular coupling took about 2 min and SAPV preceded RRV by about 0.85 s during the whole test. The analysis of the Eurobavar data set, which includes subjects with intact as well as impaired baroreflex, showed that the presented methodology represents an improved TF generalization of traditional time-invariant methodologies and can reveal dysfunctions in subjects with baroreflex impairment. Additionally, the results also suggest the use of non-stationary signal-processing techniques to analyze signals recorded under conditions that are usually supposed to be stationary.

Time-frequency Analysis on low-resistivity Shielding Layer in TEM Soundings

The transient electromagnetic (TEM) method will be influenced by shielding effect of the low-resistivity overburden layer. By adopting the smooth pseudo Wigner-Ville distribution (SPWD), the responses simulated with a finite-difference time-domain method (FDTD) of D- and G-type models by a 2D line source and H-, A-, K- and Q-type models by a loop source are transformed to the time-frequency (T-F) plane. It is indicated that in low-resistivity, the TEM wave aggregates and will consume more energy, it transmits faster in high-resistivity layers but slower in low-resistivity ones. For A-type models widely in distribution of the North China type coalfield of our country, energy of the TEM field has been almost depleted when arriving at the bottom interface (interfaces of Ordovician limestone and coal series) during the TEM exploration in this area, influence of the low resistive shielding layer shall be taken into full consideration, and relatively longer observing time window shall be selected to ensure the detection depth and high-power instruments shall be adopted to increase the signal-noise ratio during construction design.

Joint signal parameter estimation of frequency-hopping communications

In the problem of the parameter estimation of frequency-hopping (FH) signals, most of existing works can only provide the unauthorised detection of the FH signals or estimate the part of parameters of FH signals, therefore cannot provide sufficient information to demodulate signals for message deciphering applications in a non-cooperative communications. This study proposes a new method based on reassigned smoothed pseudo Wigner-Ville distribution (SPWVD) and maximum-likelihood estimation for joint signal parameter estimation of FH communications with M -ary frequency-shift-keyed (MFSK) orthogonal modulation. With the good time frequency concentration and restraining cross-term ability of reassigned SPWVD, this algorithm can efficiently estimate the parameters of FH signals which include hopping frequencies, hopping rate, hopping sequence and modulation type without making any assumption about the alphabet of hopping frequencies or the synchronisation. The algorithm has improved estimation accuracy, reduced estimation root-mean-squared error and obtained better performance than that of the approach based on conventional time-frequency distribution. The simulation results are presented to evaluate the performances of the proposed algorithm. The root-mean-squared error of hopping frequency estimation is <;10 -3 for signal-to-noise ratio (SNR) of >-2 dB. The percentage of correct modulation recognition goes to 90% when SNR >3 dB.

Characterization of Dynamic Interactions Between Cardiovascular Signals by Time-Frequency Coherence

An assessment of the dynamic interactions between cardiovascular signals can provide valuable information to improve the understanding of cardiovascular control. In this study, two methodologies for the characterization of time-frequency (TF) coherence between cardiovascular signals are described. The methodologies are based on the smoothed pseudo-Wigner-Ville distribution (SPWVD) and multitaper spectrogram (MTSP), and include the automatic assessment of the significance level of coherence estimates. The capability to correctly localize TF regions, where signals are locally coupled, is assessed using computer-generated data, and data from healthy volunteers. The SPWVD allows for the localization of these regions with higher accuracy (AC > 96.9% for SNR ≥ 5 dB) than the MTSP (AC > 84.4% for SNR ≥ 5 dB). In 14 healthy subjects, TF coherence analysis was used to describe the changes, which a tilt table test provokes in the cardiovascular control. Orthostatic stress provoked an increase in the coupling between R-R variability (RRV) and systolic arterial pressure variability; it did not provoke any significant changes in the coupling between RRV and respiration. In HF band, it decreased the strength of the coupling between RRV and pulse interval variability estimated from arterial pressure signal.

A parameter estimation method for FH signal based on SPWVD

A parameter estimation method for frequency hopping (FH) signal in low signal-to-noise ratio (SNR) circumstance is proposed by using the derivation of the time-frequency backbone, overlapped multiple windows and iteration-based adaptive-threshold based on smoothed pseudo wigner-ville distribution (SPWVD). Through the derivation process of the time-frequency backbone, the mutation pulses are presented at the hopping times, so that the hopping features are magnified. With the help of iteration-based adaptive-threshold method, the false hopping points are removed, and the hop duration can be calculated with the mutation pulses. The simulation result shows that better estimation performance could be achieved at low SNR, which is improved about 8 dB compared with the traditional method.

Instantaneous venous oxygenation estimation using the Photoplethysmograph (PPG) waveform

In this study oesophageal photoplethysmograph data from eight patients under positive pressure ventilation were analysed in order to test the hypothesis that the modulations created by the ventilation in the AC Photoplethysmograph (PPG) signal could be used to estimate venous oxygen saturation. In order to estimate the instantaneous arterial and venous oxygen saturation Smoothed-pseudo Wigner-Ville Distribution (SPWVD) was utilised. The result from this study showed that there was no significant different in the conventional (time domain) arterial saturation and the instantaneous arterial saturation. However, the instantaneous venous oxygen saturation estimated with the ventilator modulation were significantly lower then the conventional arterial saturation (P = 0.008) and also from the instantaneous arterial saturation (P = 0.008).

Locating all the Frequency Hopping Components Using Multi-species Particle Swarm Optimization

The particle swarm optimization (PSO) algorithm is applied to the problem of blind parameter estimation of frequency hopping signals. For this target, one Time Frequency representation such as Smoothed Pseudo Wigner-Ville Distribution (SPWVD) is computed firstly. Then, the peaks on TF plane are searched using multi- species PSO. Each particle moves around two dimension time and frequency plane and will converge to different species, which seeds represent the centers of frequency hopping components. A numerical study is carried out for signals which are embedded in a very low SNR ratio noise. Results show that the new method is feasible and much more robust than some existing estimation algorithms.

Comparison between Wigner–Ville distribution- and empirical mode decomposition vibration-based techniques for helical gearbox monitoring

This article presents a comparison between empirical mode decomposition (EMD) and smoothed pseudo-Wigner–Ville distribution (SPWVD) methods based on vibration signature and energy calculation procedure for monitoring gearbox systems. The simulation and experimental work were carried out using two-stage helical gears for a healthy pair of gears and a pair suffering from a tooth breakage with severity fault 1 (25 per cent tooth removal), fault 2 (50 per cent tooth removal), fault 3 (75 per cent tooth removal), and fault 4 (100 per cent tooth removal) under loads (0, 20, 40, 60, and 80 per cent of the total load) and speeds (10, 30, 50, 70, and 90 per cent of full speed). This article illustrates that the calculation of energy using EMD techniques offers a more effective way to detect early faults than that computations using the SPWVD method, and that the computation of energy using the EMD technique is faster than the calculations done using the SPWVD method.

Synthesis of HRV signals characterized by predetermined time-frequency structure by means of time-varying ARMA models

AbstractIn this paper we present two methodologies to generate heart rate variability (HRV) signals characterized by controlled and real-like time-frequency (TF) structure to be used to assess different methods of non-stationary HRV analysis. The synthesized signals are stochastic processes whose TF structure is predetermined by choosing either the time-course of the instantaneous frequencies and powers or the shape of the TF model function. They consist of three steps: (a) choice of the desired TF structure of the signals by choosing a set of design parameters; (b) automatic identification of the parameters of the corresponding models via simple closed-form expressions; (c) synthesis of the desired stochastic signals. Two measures to evaluate the goodness of the simulated signals are also given. Using this framework we were able to model the wide range of non-stationarities observed in heart rate modulation during exercise stress testing and experiments of music-induced emotions. We used the proposed methodology to assess the capability of the smoothed pseudo Wigner–Ville distribution (SPWVD) to quantify HRV patterns. We observed that the SPWVD followed the temporal evolution of the spectral components even when sudden and sharp transitions occur.